Optimal. Leaf size=22 \[ 3 e^{4-x} x+e^{-e^4+x} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(48\) vs. \(2(22)=44\).
time = 0.04, antiderivative size = 48, normalized size of antiderivative = 2.18, number of steps
used = 6, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {12, 2207, 2225}
\begin {gather*} -3 e^{4-x} (1-x)+3 e^{4-x}-e^{x-e^4}+e^{x-e^4} (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-e^4} \int \left (e^{4+e^4-x} (3-3 x)+e^x (1+x)\right ) \, dx\\ &=e^{-e^4} \int e^{4+e^4-x} (3-3 x) \, dx+e^{-e^4} \int e^x (1+x) \, dx\\ &=-3 e^{4-x} (1-x)+e^{-e^4+x} (1+x)-e^{-e^4} \int e^x \, dx-\left (3 e^{-e^4}\right ) \int e^{4+e^4-x} \, dx\\ &=3 e^{4-x}-e^{-e^4+x}-3 e^{4-x} (1-x)+e^{-e^4+x} (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 22, normalized size = 1.00 \begin {gather*} 3 e^{4-x} x+e^{-e^4+x} x \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(50\) vs.
\(2(21)=42\).
time = 0.04, size = 51, normalized size = 2.32
method | result | size |
risch | \({\mathrm e}^{x -{\mathrm e}^{4}} x +3 x \,{\mathrm e}^{-x +4}\) | \(20\) |
norman | \(\left (x \,{\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{2 x}+3 x \,{\mathrm e}^{4}\right ) {\mathrm e}^{-x}\) | \(23\) |
default | \({\mathrm e}^{-{\mathrm e}^{4}} {\mathrm e}^{x}+{\mathrm e}^{-{\mathrm e}^{4}} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )-3 \,{\mathrm e}^{-x} {\mathrm e}^{4}-3 \,{\mathrm e}^{4} \left (-x \,{\mathrm e}^{-x}-{\mathrm e}^{-x}\right )\) | \(51\) |
meijerg | \(-\frac {3 \,{\mathrm e}^{-x +4-x \,{\mathrm e}^{-{\mathrm e}^{4}}} {\mathrm e}^{2 x} \left (1-\frac {\left (2 x \left (2-{\mathrm e}^{-{\mathrm e}^{4}}\right )+2\right ) {\mathrm e}^{-x \left (2-{\mathrm e}^{-{\mathrm e}^{4}}\right )}}{2}\right )}{\left (2-{\mathrm e}^{-{\mathrm e}^{4}}\right )^{2}}+\frac {3 \,{\mathrm e}^{-x +4-x \,{\mathrm e}^{-{\mathrm e}^{4}}} {\mathrm e}^{2 x} \left (1-{\mathrm e}^{-x \left (2-{\mathrm e}^{-{\mathrm e}^{4}}\right )}\right )}{2-{\mathrm e}^{-{\mathrm e}^{4}}}+{\mathrm e}^{-x -x \,{\mathrm e}^{-{\mathrm e}^{4}}+{\mathrm e}^{4}} {\mathrm e}^{2 x} \left (1-\frac {\left (-2 x \,{\mathrm e}^{-{\mathrm e}^{4}}+2\right ) {\mathrm e}^{x \,{\mathrm e}^{-{\mathrm e}^{4}}}}{2}\right )-{\mathrm e}^{-x -x \,{\mathrm e}^{-{\mathrm e}^{4}}} {\mathrm e}^{2 x} \left (1-{\mathrm e}^{x \,{\mathrm e}^{-{\mathrm e}^{4}}}\right )\) | \(185\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 40 vs.
\(2 (19) = 38\).
time = 0.26, size = 40, normalized size = 1.82 \begin {gather*} {\left (3 \, {\left (x e^{\left (e^{4} + 4\right )} + e^{\left (e^{4} + 4\right )}\right )} e^{\left (-x\right )} + x e^{x} - 3 \, e^{\left (-x + e^{4} + 4\right )}\right )} e^{\left (-e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 30, normalized size = 1.36 \begin {gather*} {\left (3 \, x e^{\left (-2 \, x + 2 \, e^{4} + 12\right )} + x e^{\left (e^{4} + 8\right )}\right )} e^{\left (x - 2 \, e^{4} - 8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 24, normalized size = 1.09 \begin {gather*} \frac {x e^{x} + 3 x e^{4} e^{- x} e^{e^{4}}}{e^{e^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 37, normalized size = 1.68 \begin {gather*} {\left (x e^{x} + 3 \, {\left (x - e^{4}\right )} e^{\left (-x + e^{4} + 4\right )} + 3 \, e^{\left (-x + e^{4} + 8\right )}\right )} e^{\left (-e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 19, normalized size = 0.86 \begin {gather*} 3\,x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^4+x\,{\mathrm {e}}^{-{\mathrm {e}}^4}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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